WASHINGTON (CNN) -- A senior al Qaeda leader -- described as the group's "chief of operations in the Arabian Peninsula" -- was killed in a shootout in Saudi Arabia, U.S. officials have told CNN.

A U.S. counterterrorism official called the death on Monday "very significant, and a major blow to al Qaeda."

The man was identified as Abu Hazim al-Sha'ir, also known as Kahlid Ali Hajj. He was also nicknamed "the poet," officials said.

"This was a very significant senior al Qaeda figure in Saudi Arabia," the counterterrorism official said.

Hajj, originally from Yemen, has been sought since May, when Saudi officials put his name on a list of men wanted for questioning just before the triple suicide bombings in the capital city of Riyadh, according to Reuters.

The May bombings killed 23 people -- most of them Westerners -- at three housing complexes in Riyadh. In November, suicide bombers killed 18 people in a different housing compound in the capital.

Last month, Saudi authorities warned that a militant may be planning a new car bomb attack in Riyadh.

In its statement published by the Saudi Press Agency, the Interior Ministry described a vehicle that might be involved in an attack and asked people to be on alert, especially those who live in the capital

The Saudi warning promised financial rewards for information about the suspect and his car.

In January, an audiotape purportedly from bin Laden called on Muslims to lead a jihad against Middle East leaders cooperating with the United States. The voice on the tape mentioned the November bombing in Riyadh.